How to best learn the math you need?

Use six steps to learn a math skill.  Our new learning materials supports this recommended process.

-1-   EXPLORE   Develop a genuine, enthusiastic curiosity –  become a true mental explorer. Develop this enthusiasm so you will persist in the mental effort to focus attention, understand connections, avoid confusion,  get help for difficulties and overcome inevitable discouragements.

-2-   INQUIRE   Keep formulating inquiry questions –check on what you know and what you don’t know.  Persist in seeking answers to these questions. Use the 5W2H question stems:  Who -, What -, When -, Where -, Why -, How -, How much -?

-3-   CONNECT    your new learning material items to integrate them with the old material items you already learned. Recognize and master all prerequisites first.

-4-   MODEL   Adapt/create mental models to summarize thr new knowledge, contrast similarities and differences and connect knowledge items. Create these models as schema for effective comprehension and improved recall.

-5-   INTERLEAVE   review topics to focus on summary understanding and of differences and similarities.

-6-   SPACE  practice for active recall of these connection models, summaries, concepts, examples and skills.  Do this for long term retention through repeated, directed self-quizzing of your own (for example, Cornell Notes) or our prepared materials.

Mathematically Gifted Students

Some students are able to keep up with their class learning.  They are A or B students. They need standard guidance for after-class practice.

Other students are having difficulty keeping up with their class.  These students cannot maintain either an A or B grade.  They need customized guidance for after-class practice.for remediation, reteaching and

Some students simply are not able to keep up with the class pace and are determined to have special education needs.  They need highly customized guidance

There are a few mathematically gifted students who also need highly customized guidance for after-class practice. The goal here is to achieve mastery, maintain it and challenge for advancement.
See more on Mathematically Gifted Students




Learning Styles: What role should they play?

Many students misunderstand the  concept of “learning style” and its role in learning mathematics.  There are no “fixed styles you are born with”.  Learning style preferences are not fixed and can be changed.  They should be used selectively to support meeting your learning goals in many different contexts.

There are seven “learning style preferences”.

Visual (spatial): You prefer using pictures, images, and spatial understanding.

Aural (auditory-musical):  You prefer using sound and music.

Verbal (linguistic):  You prefer using words, both in speech and writing.

Physical (kinesthetic):  You prefer using your body, hands and sense of touch.

Logical (mathematical):  You prefer using logic, reasoning and systems.

Social (inter-personal):  You prefer to learn in groups or with other people.

Solitary (intra-personal): You prefer to work alone and use self-study.

You can find out what your current preferences are by taking a simple inventory, as here.

Get beyond the notion that your learning depends solely on not satisfying your “preferred learning style”.

Your preferences are not fixed – they can be changed.  Your success in learning

You can use the different preference styles in many ways to learn the mathematics you need. Ultimately you will need to work alone and responsible for your selfstudy program.

Be the one in charge of your own learning.

Mastery is a quest , especially of complex ideas, skills, and processes, .

Get beyond”learning style preferences” and embrace the notion of successful intelligence.

Describe what you want to know, do, or accomplish. Then list the competencies required, what you need to learn, and where you can find the knowledge or skill. Then go get it.

Consider your expertise to be in a state of continuing development.

Practice self- testing as a learning strategy to discover your strengths and weaknesses.

Build on your strengths. Then focus becoming more competent on improving yourself in the weakness areas.

Adopt active learning strategies like retrieval practice , spacing, and interleaving. Be aggressive.

Don’t rely on what feels best:  use quizzing, peer review, and  other tools such as journals

Maintain your enthusiasm for learning.  Remember that the difficulties you can overcome with more cognitive effort will more than repay you in the strength of your learning.


Analyze your learning objectives and the needed knowledge structure.

Define your learning objectives explicitly.

Understand the context of your learning objectives.

Break down each one into their component parts.

Carefully build the knowledge structure that addresses them.

Then summarize and represent that structure

If you’re an example learner, study examples two at a time or more, rather than one by one, asking yourself in what ways they are alike and different. Are the differences such that they require different solutions, or are the similarities such that they respond to a common solution?

If you think you are a low structure-builder or an example learner trying to learn new material, pause periodically and ask what the central ideas are, what the rules are.

Describe each idea and recall the related points. Which are the big ideas, and which are supporting concepts or nuances? If you were to test yourself on the main ideas, how would you describe them?

What kind of scaffold or framework can you imagine that holds these central ideas together?

As in concept formation by abstracting the underlying rules and piecing them into a structure, you go then use it both to increase knowledge – but also for more than knowledge – your know-how skills.

And that kind of mastery will put you ahead.


Brown, Peter C. (2014-04-14). Make It Stick (p. 161). Harvard University Press. Kindle Edition.